The paper provides constant-factor approximation algorithms for Max Dist-2 Independent Set and Min Dominating Set in graphs of bounded radius-2 merge-width.

This paper studies the maximum size of an independent set in the discrete simplex graph and provides new bounds using translated smaller graphs and finite rational linear systems.

The paper removes stability requirement from the progressive exploration algorithm for Dominating Set, yielding a fixed-parameter tractable algorithm on certain graph classes.

This paper establishes a finite combinatorial version of Gödel's incompleteness theorems in Boolean $K$-SAT, resolving assignment correlations and constructing structurally irreducible SAT/UNSAT pairs…

This paper provides bounds on the difference between the annihilation number and independence number of a finite simple graph, and proves these bounds for various types of graphs.

The paper shows that syntactic separation implies computational indistinguishability in local syntactic systems, proving new derivation-length and cryptographic bounds.

The paper provides a constructive, intuitionistically valid proof of Rice's Theorem and the Halting Problem undecidability by reducing the problem to the undecidability of Hilbert's Tenth Problem (MRD…

This paper studies the NP-completeness and provides a polynomial-time algorithm for the disjoint separators problem in planar graphs when all sizes are equal to one.

This paper studies the decidability and complexity properties of unary three-way and two-way deterministic and nondeterministic two-dimensional automata.

This paper investigates the complexity of recognizing domatically critical graphs, which are graphs with maximum dominating sets that cannot be increased by deleting any edge.

This paper shows that finite unions of intersecting affine modules in one dimension are efficiently exactly learnable using equivalence and subset queries.

This paper proposes a framework for multi-hop retrieval as query-set compatibility scoring, improving retrieval performance and downstream QA task performance.

The paper provides tight bounds for the OR-rank and an upper bound for the SUM-rank of the unique disjointness matrix.

This paper identifies a technical oversight in Mossel and Peres (2005) theorem on designing Bernoulli factories for multivariable functions and provides a counterexample.

This paper introduces a structural theorem for the sparsifiability of real-valued codes, which generalizes both combinatorial and continuous notions of sparsification.

This paper presents deterministic and randomized algorithms for the incremental dominating set problem in vertex-weighted graphs, achieving competitive ratios of O(Δ) and O(log^2Δ) respectively. It al…

This paper introduces the Value Causal Markov Condition (v-CMC) for linking causality and utility, and develops its foundations.